“I had a total panic attack,” Twain, 45, speaking at her new home in the Bahamas, tells PEOPLE in an exclusive interview. “I just told her that she was a bad person – that’s all I could get out!”

“When I left her, I thought [to myself], ‘You’re such a wimp, you coward!’ ” Twain recalls with a laugh. “That was my big moment, and I blew it!”

All that is past history, as Twain has had her own second chance at love – with Thiébaud’s ex-husband, Fred, 40.

Wed on New Year’s Day in Puerto Rico, the couple are relishing their newlywed life, even while Twain hits the road to promote her new memoir, From This Moment On, and a docu-series on Oprah Winfrey‘s OWN Network, Why Not? with Shania Twain.

“Fred,” says Twain, “has given me a second lease on love.”

For more on Twain’s surviving the betrayal and finding love again – plus, an exclusive book excerpt – pick up the new issue of PEOPLE, on newsstands Friday